A theory of multi-perspective defocusing

We present a novel theory for characterizing defocus blurs in multi-perspective cameras such as catadioptric mirrors. Our approach studies how multi-perspective ray geometry transforms under the thin lens. We first use the General Linear Cameras (GLCs) to approximate the incident multi-perspective rays to the lens and then apply a Thin Lens Operator (TLO) to map an incident GLC to the exit GLC. To study defocus blurs caused by the GLC rays, we further introduce a new Ray Spread Function (RSF) model analogous the Point Spread Function (PSF). While PSF models defocus blurs caused by a 3D scene point, RSF models blurs spread by rays. We derive closed form RSFs for incident GLC rays, and we show that for catadioptric cameras with a circular aperture, the RSF can be effectively approximated as a single or mixtures of elliptic-shaped kernels. We apply our method for predicting defocus blurs on commonly used catadioptric cameras and for reducing de-focus blurs in catadioptric projections. Experiments on synthetic and real data demonstrate the accuracy and general applicability of our approach.